Analysis of 111/999 NHS calls and 111 online reports
Quentin Leclerc, Emily Nightingale, Samuel Abbott & Thibaut Jombart, for CMMID
Friday 02 October 2020
1 Data preparation
1.1 Outline
Load scripts: loads libraries and useful scripts used in the analyses; all
.Rfiles contained inscriptsat the root of the factory are automatically loadedLoad data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.
1.2 Load packages
library(reportfactory)
library(here)
library(rio)
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)1.3 Load scripts
These scripts will load:
- all scripts stored as
.Rfiles inside/scripts/ - all scripts stored as
.Rfiles inside/src/
These scripts also contain routines to access the latest clean encrypted data (see next section).
1.4 Load clean data
We import the latest NHS pathways data:
x <- import_pathways() %>%
as_tibble()
x
## [90m# A tibble: 268,529 x 11[39m
## site_type date sex age ccg_code ccg_name count postcode nhs_region
## [3m[90m<chr>[39m[23m [3m[90m<date>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<int>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m
## [90m 1[39m 111 2020-03-18 fema… miss… e380000… nhs_glo… 1 gl34fe South West
## [90m 2[39m 111 2020-03-18 fema… miss… e380001… nhs_sou… 1 ne325nn North Eas…
## [90m 3[39m 111 2020-03-18 fema… 0-18 e380000… nhs_air… 8 bd57jr North Eas…
## [90m 4[39m 111 2020-03-18 fema… 0-18 e380000… nhs_ash… 7 tn254ab South East
## [90m 5[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bar… 35 rm13ae London
## [90m 6[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bar… 9 n111np London
## [90m 7[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bar… 11 s752py North Eas…
## [90m 8[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bas… 19 ss143hg East of E…
## [90m 9[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bas… 6 dn227xf North Eas…
## [90m10[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bat… 9 ba25rp South West
## [90m# … with 268,519 more rows, and 2 more variables: day [3m[90m<int>[90m[23m, weekday [3m[90m<fct>[90m[23m[39mWe also import demographics data for NHS regions in England, used later in our analysis:
path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
## nhs_region variable value
## 1 North West 0-18 0.22538599
## 2 North East and Yorkshire 0-18 0.21876449
## 3 Midlands 0-18 0.22564656
## 4 East of England 0-18 0.22810783
## 5 London 0-18 0.23764782
## 6 South East 0-18 0.22458811
## 7 South West 0-18 0.20799797
## 8 North West 19-69 0.64274078
## 9 North East and Yorkshire 19-69 0.64437753
## 10 Midlands 19-69 0.63876675
## 11 East of England 19-69 0.63034229
## 12 London 19-69 0.67820084
## 13 South East 19-69 0.63267336
## 14 South West 19-69 0.63176131
## 15 North West 70-120 0.13187323
## 16 North East and Yorkshire 70-120 0.13685797
## 17 Midlands 70-120 0.13558669
## 18 East of England 70-120 0.14154988
## 19 London 70-120 0.08415135
## 20 South East 70-120 0.14273853
## 21 South West 70-120 0.16024072Finally, we import publically available deaths per NHS region:
dth <- import_deaths() %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
#truncation to account for reporting delay
delay_max <- 21
dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
## date_report nhs_region deaths
## 1 2020-03-01 East of England 0
## 2 2020-03-02 East of England 1
## 3 2020-03-03 East of England 0
## 4 2020-03-04 East of England 0
## 5 2020-03-05 East of England 0
## 6 2020-03-06 East of England 1
## 7 2020-03-07 East of England 0
## 8 2020-03-08 East of England 0
## 9 2020-03-09 East of England 1
## 10 2020-03-10 East of England 0
## 11 2020-03-11 East of England 0
## 12 2020-03-12 East of England 0
## 13 2020-03-13 East of England 1
## 14 2020-03-14 East of England 2
## 15 2020-03-15 East of England 2
## 16 2020-03-16 East of England 1
## 17 2020-03-17 East of England 1
## 18 2020-03-18 East of England 5
## 19 2020-03-19 East of England 4
## 20 2020-03-20 East of England 2
## 21 2020-03-21 East of England 11
## 22 2020-03-22 East of England 12
## 23 2020-03-23 East of England 11
## 24 2020-03-24 East of England 19
## 25 2020-03-25 East of England 26
## 26 2020-03-26 East of England 36
## 27 2020-03-27 East of England 38
## 28 2020-03-28 East of England 28
## 29 2020-03-29 East of England 43
## 30 2020-03-30 East of England 45
## 31 2020-03-31 East of England 70
## 32 2020-04-01 East of England 62
## 33 2020-04-02 East of England 65
## 34 2020-04-03 East of England 80
## 35 2020-04-04 East of England 71
## 36 2020-04-05 East of England 76
## 37 2020-04-06 East of England 71
## 38 2020-04-07 East of England 93
## 39 2020-04-08 East of England 111
## 40 2020-04-09 East of England 87
## 41 2020-04-10 East of England 74
## 42 2020-04-11 East of England 92
## 43 2020-04-12 East of England 100
## 44 2020-04-13 East of England 78
## 45 2020-04-14 East of England 61
## 46 2020-04-15 East of England 82
## 47 2020-04-16 East of England 74
## 48 2020-04-17 East of England 86
## 49 2020-04-18 East of England 64
## 50 2020-04-19 East of England 67
## 51 2020-04-20 East of England 67
## 52 2020-04-21 East of England 75
## 53 2020-04-22 East of England 67
## 54 2020-04-23 East of England 49
## 55 2020-04-24 East of England 66
## 56 2020-04-25 East of England 54
## 57 2020-04-26 East of England 48
## 58 2020-04-27 East of England 46
## 59 2020-04-28 East of England 58
## 60 2020-04-29 East of England 32
## 61 2020-04-30 East of England 45
## 62 2020-05-01 East of England 49
## 63 2020-05-02 East of England 29
## 64 2020-05-03 East of England 41
## 65 2020-05-04 East of England 19
## 66 2020-05-05 East of England 36
## 67 2020-05-06 East of England 31
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## 69 2020-05-08 East of England 33
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## 77 2020-05-16 East of England 26
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## 79 2020-05-18 East of England 25
## 80 2020-05-19 East of England 15
## 81 2020-05-20 East of England 26
## 82 2020-05-21 East of England 21
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## 84 2020-05-23 East of England 12
## 85 2020-05-24 East of England 17
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## 146 2020-07-24 East of England 1
## 147 2020-07-25 East of England 0
## 148 2020-07-26 East of England 1
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## 151 2020-07-29 East of England 0
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## 1152 2020-05-21 South East 15
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## 1223 2020-07-31 South East 1
## 1224 2020-08-01 South East 2
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## 1226 2020-08-03 South East 0
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## 1230 2020-08-07 South East 0
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## 1249 2020-08-26 South East 0
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## 1253 2020-08-30 South East 0
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## 1255 2020-09-01 South East 1
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## 1257 2020-09-03 South East 0
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## 1261 2020-09-07 South East 0
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## 1266 2020-09-12 South East 0
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## 1272 2020-09-18 South East 1
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## 1274 2020-09-20 South East 0
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## 1276 2020-09-22 South East 0
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## 1278 2020-09-24 South East 0
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## 1281 2020-09-27 South East 2
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## 1283 2020-09-29 South East 2
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## 1285 2020-03-01 South West 0
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## 1299 2020-03-15 South West 0
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## 1373 2020-05-28 South West 10
## 1374 2020-05-29 South West 7
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## 1382 2020-06-06 South West 1
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## 1385 2020-06-09 South West 0
## 1386 2020-06-10 South West 1
## 1387 2020-06-11 South West 2
## 1388 2020-06-12 South West 2
## 1389 2020-06-13 South West 2
## 1390 2020-06-14 South West 0
## 1391 2020-06-15 South West 2
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## 1393 2020-06-17 South West 0
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## 1395 2020-06-19 South West 0
## 1396 2020-06-20 South West 2
## 1397 2020-06-21 South West 0
## 1398 2020-06-22 South West 1
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## 1400 2020-06-24 South West 1
## 1401 2020-06-25 South West 0
## 1402 2020-06-26 South West 3
## 1403 2020-06-27 South West 0
## 1404 2020-06-28 South West 0
## 1405 2020-06-29 South West 1
## 1406 2020-06-30 South West 0
## 1407 2020-07-01 South West 0
## 1408 2020-07-02 South West 0
## 1409 2020-07-03 South West 0
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## 1411 2020-07-05 South West 1
## 1412 2020-07-06 South West 0
## 1413 2020-07-07 South West 0
## 1414 2020-07-08 South West 2
## 1415 2020-07-09 South West 0
## 1416 2020-07-10 South West 1
## 1417 2020-07-11 South West 0
## 1418 2020-07-12 South West 0
## 1419 2020-07-13 South West 1
## 1420 2020-07-14 South West 0
## 1421 2020-07-15 South West 0
## 1422 2020-07-16 South West 0
## 1423 2020-07-17 South West 1
## 1424 2020-07-18 South West 0
## 1425 2020-07-19 South West 0
## 1426 2020-07-20 South West 0
## 1427 2020-07-21 South West 0
## 1428 2020-07-22 South West 0
## 1429 2020-07-23 South West 0
## 1430 2020-07-24 South West 0
## 1431 2020-07-25 South West 0
## 1432 2020-07-26 South West 0
## 1433 2020-07-27 South West 0
## 1434 2020-07-28 South West 0
## 1435 2020-07-29 South West 0
## 1436 2020-07-30 South West 1
## 1437 2020-07-31 South West 0
## 1438 2020-08-01 South West 0
## 1439 2020-08-02 South West 0
## 1440 2020-08-03 South West 0
## 1441 2020-08-04 South West 0
## 1442 2020-08-05 South West 0
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## 1445 2020-08-08 South West 0
## 1446 2020-08-09 South West 0
## 1447 2020-08-10 South West 0
## 1448 2020-08-11 South West 0
## 1449 2020-08-12 South West 0
## 1450 2020-08-13 South West 0
## 1451 2020-08-14 South West 1
## 1452 2020-08-15 South West 0
## 1453 2020-08-16 South West 0
## 1454 2020-08-17 South West 2
## 1455 2020-08-18 South West 0
## 1456 2020-08-19 South West 0
## 1457 2020-08-20 South West 0
## 1458 2020-08-21 South West 0
## 1459 2020-08-22 South West 0
## 1460 2020-08-23 South West 0
## 1461 2020-08-24 South West 0
## 1462 2020-08-25 South West 1
## 1463 2020-08-26 South West 0
## 1464 2020-08-27 South West 1
## 1465 2020-08-28 South West 0
## 1466 2020-08-29 South West 0
## 1467 2020-08-30 South West 0
## 1468 2020-08-31 South West 0
## 1469 2020-09-01 South West 0
## 1470 2020-09-02 South West 0
## 1471 2020-09-03 South West 0
## 1472 2020-09-04 South West 0
## 1473 2020-09-05 South West 0
## 1474 2020-09-06 South West 0
## 1475 2020-09-07 South West 0
## 1476 2020-09-08 South West 1
## 1477 2020-09-09 South West 0
## 1478 2020-09-10 South West 0
## 1479 2020-09-11 South West 0
## 1480 2020-09-12 South West 0
## 1481 2020-09-13 South West 0
## 1482 2020-09-14 South West 0
## 1483 2020-09-15 South West 0
## 1484 2020-09-16 South West 0
## 1485 2020-09-17 South West 1
## 1486 2020-09-18 South West 0
## 1487 2020-09-19 South West 0
## 1488 2020-09-20 South West 1
## 1489 2020-09-21 South West 0
## 1490 2020-09-22 South West 0
## 1491 2020-09-23 South West 0
## 1492 2020-09-24 South West 0
## 1493 2020-09-25 South West 0
## 1494 2020-09-26 South West 0
## 1495 2020-09-27 South West 0
## 1496 2020-09-28 South West 0
## 1497 2020-09-29 South West 0
## 1498 2020-09-30 South West 01.5 Completion date
We extract the completion date from the NHS Pathways file timestamp:
The completion date of the NHS Pathways data is Thursday 01 Oct 2020.
1.6 Auxiliary functions
These are functions which will be used further in the analyses.
Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:
## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here
Rsq <- function(x) {
1 - (x$deviance / x$null.deviance)
}Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:
## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals
get_r <- function(model) {
## extract coefficients and conf int
out <- data.frame(r = coef(model)) %>%
rownames_to_column("var") %>%
cbind(confint(model)) %>%
filter(!grepl("day_of_week", var)) %>%
filter(grepl("day", var)) %>%
rename(lower_95 = "2.5 %",
upper_95 = "97.5 %") %>%
mutate(var = sub("day:", "", var))
## reconstruct values: intercept + region-coefficient
for (i in 2:nrow(out)) {
out[i, -1] <- out[1, -1] + out[i, -1]
}
## find the name of the intercept, restore regions names
out <- out %>%
mutate(nhs_region = model$xlevels$nhs_region) %>%
select(nhs_region, everything(), -var)
## find halving times
halving <- log(0.5) / out[,-1] %>%
rename(halving_t = r,
halving_t_lower_95 = lower_95,
halving_t_upper_95 = upper_95)
## set halving times with exclusion intervals to NA
no_halving <- out$lower_95 < 0 & out$upper_95 > 0
halving[no_halving, ] <- NA_real_
## return all data
cbind(out, halving)
}Functions used in the correlation analysis between NHS Pathways reports and deaths:
## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.
getcor <- function(x, ndx) {
return(cor(x$deaths[ndx],
x$note_lag[ndx],
use = "complete.obs",
method = "pearson"))
}
## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)
getboot <- function(x) {
result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000),
type = "bca")
return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
r = result$t0,
r_low = result$bca[4],
r_hi = result$bca[5]))
}Function to classify the day of the week into weekend, Monday, and the rest:
## Fn to add day of week
day_of_week <- function(df) {
df %>%
dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>%
dplyr::mutate(day_of_week = dplyr::case_when(
day_of_week %in% c("Sat", "Sun") ~ "weekend",
day_of_week %in% c("Mon") ~ "monday",
!(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
) %>%
factor(levels = c("rest_of_week", "monday", "weekend")))
}Custom color palettes, color scales, and vectors of colors:
2 Temporal trends in NHS Pathways reports
2.1 Outline
We look for temporal patterns in COVID-19 related 111/999 calls and 111 online reports. Analyses are broken down by NHS region. We also look for estimates of recent growth rate and associated doubling / halving time.
2.2 Reports by region over time
tab_date_region_all <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
dth %>%
mutate(trusted = case_when(date_report < max(dth$date_report)-delay_max ~ "Y",
date_report >= max(dth$date_report)-delay_max ~ "N"),
value = "Deaths",
vline = max(dth$date_report)-delay_max-1,
lab = "Truncated for reporting delay",
lab_pos_x = vline + 10,
lab_pos_y = 150,
lab_col = "darkgrey") %>%
rename(date = date_report,
n = deaths) %>%
bind_rows(
mutate(tab_date_region_all, value = "Reports",
trusted = "Y",
vline = as.Date("2020-03-23"),
lab = "Start of UK lockdown",
lab_pos_x = vline - 8,
lab_pos_y = 30200,
lab_col = "black")
) %>%
mutate(value = factor(value, levels = c("Reports","Deaths"))) -> dths_reports
plot_dth_report <-
ggplot(dths_reports, aes(date, n, colour = nhs_region)) +
# Add main points and lines, coloured by region and fade out deaths for excluded period
geom_point(aes(alpha = trusted)) +
geom_line(alpha = 0.2) +
geom_smooth(method = "loess", span = .5, color = "black") +
scale_colour_manual("", values = pal) +
scale_alpha_manual(values = c(0.3,1)) +
guides(alpha = F) +
# Add vertical markers for important dates with labels - different for each facet
ggnewscale::new_scale_colour() +
geom_vline(aes(xintercept = vline, col = value), lty = "solid") +
geom_text(aes(x = lab_pos_x, y = lab_pos_y, label = lab, col = value), size = 3) +
scale_colour_manual("",values = c("black","darkgrey"), guide = F) +
# Facet by deaths and reports
facet_grid(rows = vars(value), scales = "free_y", switch = "y") +
# Other formatting
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",strip.placement = "outside") +
rotate_x +
labs(x = NULL,
y = NULL)
plot_dth_report
2.3 Reports by region by age over time
We plot the number of 111/999 calls and 111 online reports by age, and the proportion of 111/999 calls and 111 online reports by age. In the second graph, the vertical lines indicate the proportion of individuals residing in the corresponding NHS region who belong to the corresponding age group.
tab_date_region_age_all <- x %>%
filter(!is.na(nhs_region),
age != "missing") %>%
group_by(date, nhs_region, age) %>%
summarise(n = sum(count))
tab_date_region_age_all %>%
ggplot(aes(x = date, y = n, fill = age)) +
geom_col(position = "stack") +
scale_fill_manual(values = age.pal) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(fill = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Total daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
tab_date_region_age_all <- tab_date_region_age_all %>%
group_by(date, nhs_region) %>%
summarise(tot = sum(n)) %>%
left_join(tab_date_region_age_all, by = c("date", "nhs_region")) %>%
mutate(prop_n = n/tot)
tab_date_region_age_all %>%
ggplot(aes(x = date, y = prop_n, color = age)) +
scale_color_manual(values = age.pal) +
geom_line() +
geom_point() +
geom_hline(data = nhs_region_pop, aes(yintercept = value, color = variable)) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(color = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Proportion of daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
2.4 Moving window model
We fit quasi-Poisson GLMs for 14-day windows to get growth rates over time.
## set moving time window (1/2/3 weeks)
w <- 14
# create empty df
r_all_sliding <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding <- bind_rows(r_all_sliding, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding <- r_all_sliding %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))We examine the evolution of the growth rate by region over time.
# plot
plot_growth <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)From the growth rate, we derive R and examine its value through time.
# plot
plot_R <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
rotate_x +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
# strip.text.x = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "",
override.aes = list(fill = NA)),
fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))
2.5 Moving window model - stratified by age
We repeat the above analysis, where we fit quasi-Poisson GLMs for 14-day windows to get growth rates over time, but apply this to each age group separately (0-18, 19-69, 70-120 years old).
We first run the analysis for 0-18 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_0_18 <- NULL
## make data for model
x_model_all_moving_0_18 <- x %>%
filter(!is.na(nhs_region),
age == "0-18") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_0_18$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_0_18 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_0_18 <- bind_rows(r_all_sliding_0_18, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_0_18 <- r_all_sliding_0_18 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_0_18 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_0_18 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_0_18 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then, we run the analysis for 19-69 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_19_69 <- NULL
## make data for model
x_model_all_moving_19_69 <- x %>%
filter(!is.na(nhs_region),
age == "19-69") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_19_69$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_19_69 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_19_69 <- bind_rows(r_all_sliding_19_69, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_19_69 <- r_all_sliding_19_69 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_19_69 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_19_69 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_19_69 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Finally, we run the analysis for 70-120 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_70_120 <- NULL
## make data for model
x_model_all_moving_70_120 <- x %>%
filter(!is.na(nhs_region),
age == "70-120") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_70_120$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_70_120 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_70_120 <- bind_rows(r_all_sliding_70_120, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_70_120 <- r_all_sliding_70_120 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_70_120 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_70_120 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_70_120 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)"))) We combine the estimated growth rates and effective reproduction numbers into a single figure.
ggpubr::ggarrange(fig2_3_0_18,
fig2_3_19_69,
fig2_3_70_120,
nrow = 3,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom",
align = "hv") 
3 Comparison with deaths time series
3.1 Outline
We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.
Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.
3.2 Lagged correlation
We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.
First we join the NHS Pathways and death data, and aggregate over all England:
## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max
dth_trunc <- dth %>%
rename(date = date_report) %>%
filter(date <= trunc_date)
## join with notification data
all_data <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(count = sum(count, na.rm = T)) %>%
ungroup %>%
inner_join(dth_trunc,
by = c("date","nhs_region"))
all_tot <- all_data %>%
group_by(date) %>%
summarise(count = sum(count, na.rm = TRUE),
deaths = sum(deaths, na.rm = TRUE)) We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:
## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
## lag reports
summary <- all_tot %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI
getboot(.) %>%
mutate(lag = i)
lag_cor <- bind_rows(lag_cor, summary)
}
cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
theme_bw() +
geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_point() +
geom_line() +
labs(x = "Lag between NHS pathways and death data (days)",
y = "Pearson's correlation") +
large_txt
cor_vs_lag
This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.
all_tot <- all_tot %>%
rename(date_death = date) %>%
mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
date_note = lag(date_death,16))
lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")
summary(lag_mod)
##
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -21.003 -7.603 -3.445 4.382 14.272
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.907e+00 8.472e-02 46.12 <2e-16 ***
## note_lag 2.015e-05 8.784e-07 22.95 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for quasipoisson family taken to be 52.6592)
##
## Null deviance: 31481.6 on 152 degrees of freedom
## Residual deviance: 8356.7 on 151 degrees of freedom
## (23 observations deleted due to missingness)
## AIC: NA
##
## Number of Fisher Scoring iterations: 5
exp(coefficients(lag_mod))
## (Intercept) note_lag
## 49.74640 1.00002
exp(confint(lag_mod))
## 2.5 % 97.5 %
## (Intercept) 41.968566 58.509501
## note_lag 1.000018 1.000022
Rsq(lag_mod)
## [1] 0.7345539
mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])
all_tot_pred <-
all_tot %>%
filter(!is.na(note_lag)) %>%
mutate(pred = mod_fit$fit,
pred.se = mod_fit$se.fit,
low = exp(pred - 1.96*pred.se),
hi = exp(pred + 1.96*pred.se))
glm_fit <- all_tot_pred %>%
filter(!is.na(note_lag)) %>%
ggplot(aes(x = note_lag, y = deaths)) +
geom_point() +
geom_line(aes(y = exp(pred))) +
geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
theme_bw() +
labs(y = "Daily number of\ndeaths reported",
x = "Daily number of NHS Pathways reports") +
large_txt
glm_fit
4 Supplementary figures
4.1 Serial interval distribution
This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.
SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
meanlog = log(4.7),
sdlog = log(2.9), w = 0.5)
SI_dist1 <- data.frame(x = SI_distribution$r(1e5))
SI_dist1 <- count(SI_dist1, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 30, 5)) +
theme_bw()
SI_dist2 <- data.frame(x = SI_distribution2$r(1e5))
SI_dist2 <- count(SI_dist2, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
theme_bw()
ggpubr::ggarrange(SI_dist1,
SI_dist2,
nrow = 1,
labels = "AUTO") 
4.2 Sensitivity analysis - 7 or 21 days moving window
We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.
First with the 7 days window:
## set moving time window (1/2/3 weeks)
w <- 7
# create empty df
r_all_sliding_7days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)plot_R <- r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_7days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_7days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_7 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then with the 21 days window:
## set moving time window (1/2/3 weeks)
w <- 21
# create empty df
r_all_sliding_21days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_21days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_21days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_21 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))And we combine both outputs into a single plot:
ggpubr::ggarrange(r_R_7,
r_R_21,
nrow = 2,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom") 
4.3 Correlation between NHS Pathways reports and deaths by NHS region
lag_cor_reg <- data.frame()
for (i in 0:30) {
summary <-
all_data %>%
group_by(nhs_region) %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI for each region
group_modify(~getboot(.x)) %>%
mutate(lag = i)
lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}
cor_vs_lag_reg <-
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
geom_point() +
geom_line() +
facet_wrap(~nhs_region) +
scale_color_manual(values = pal) +
scale_fill_manual(values = pal, guide = F) +
theme_bw() +
labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
theme(legend.position = "bottom") +
guides(color = guide_legend(override.aes = list(fill = NA)))
cor_vs_lag_reg
5 Export data
We save the tables created during our analysis:
if (!dir.exists("excel_tables")) {
dir.create("excel_tables")
}
## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")
for (e in tables_to_export) {
rio::export(get(e),
file.path("excel_tables",
paste0(e, ".xlsx")))
}
## also export result from regression on lagged data
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))6 System information
6.1 Outline
The following information documents the system on which the document was compiled.
6.2 System
This provides information on the operating system.
Sys.info()
## sysname
## "Darwin"
## release
## "19.6.0"
## version
## "Darwin Kernel Version 19.6.0: Thu Jun 18 20:49:00 PDT 2020; root:xnu-6153.141.1~1/RELEASE_X86_64"
## nodename
## "Mac-1601633138947.local"
## machine
## "x86_64"
## login
## "root"
## user
## "runner"
## effective_user
## "runner"6.3 R environment
This provides information on the version of R used:
6.4 R packages
This provides information on the packages used:
sessionInfo()
## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.6
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] ggnewscale_0.4.3 ggpubr_0.4.0 lubridate_1.7.9
## [4] chngpt_2020.8-29 cyphr_1.1.0 DT_0.15
## [7] kableExtra_1.2.1 janitor_2.0.1 remotes_2.2.0
## [10] projections_0.5.1 earlyR_0.0.1 epitrix_0.2.2
## [13] distcrete_1.0.3 incidence_1.7.2 rio_0.5.16
## [16] reshape2_1.4.4 rvest_0.3.6 xml2_1.3.2
## [19] linelist_0.0.40.9000 forcats_0.5.0 stringr_1.4.0
## [22] dplyr_1.0.2 purrr_0.3.4 readr_1.3.1
## [25] tidyr_1.1.2 tibble_3.0.3 ggplot2_3.3.2
## [28] tidyverse_1.3.0 here_0.1 reportfactory_0.0.5
##
## loaded via a namespace (and not attached):
## [1] minqa_1.2.4 colorspace_1.4-1 selectr_0.4-2 ggsignif_0.6.0
## [5] ellipsis_0.3.1 rprojroot_1.3-2 snakecase_0.11.0 fs_1.5.0
## [9] rstudioapi_0.11 farver_2.0.3 fansi_0.4.1 splines_4.0.2
## [13] knitr_1.30 jsonlite_1.7.1 nloptr_1.2.2.2 broom_0.7.1
## [17] dbplyr_1.4.4 compiler_4.0.2 httr_1.4.2 backports_1.1.10
## [21] assertthat_0.2.1 Matrix_1.2-18 cli_2.0.2 htmltools_0.5.0
## [25] tools_4.0.2 gtable_0.3.0 glue_1.4.2 Rcpp_1.0.5
## [29] carData_3.0-4 cellranger_1.1.0 vctrs_0.3.4 nlme_3.1-148
## [33] matchmaker_0.1.1 crosstalk_1.1.0.1 xfun_0.18 openxlsx_4.2.2
## [37] lme4_1.1-23 lifecycle_0.2.0 statmod_1.4.34 rstatix_0.6.0
## [41] MASS_7.3-51.6 scales_1.1.1 hms_0.5.3 sodium_1.1
## [45] yaml_2.2.1 curl_4.3 gridExtra_2.3 stringi_1.5.3
## [49] kyotil_2020.8-22 boot_1.3-25 zip_2.1.1 rlang_0.4.7
## [53] pkgconfig_2.0.3 evaluate_0.14 lattice_0.20-41 htmlwidgets_1.5.1
## [57] labeling_0.3 cowplot_1.1.0 tidyselect_1.1.0 plyr_1.8.6
## [61] magrittr_1.5 R6_2.4.1 generics_0.0.2 DBI_1.1.0
## [65] pillar_1.4.6 haven_2.3.1 foreign_0.8-80 withr_2.3.0
## [69] mgcv_1.8-31 survival_3.1-12 abind_1.4-5 modelr_0.1.8
## [73] crayon_1.3.4 car_3.0-10 utf8_1.1.4 rmarkdown_2.4
## [77] viridis_0.5.1 grid_4.0.2 readxl_1.3.1 data.table_1.13.0
## [81] blob_1.2.1 reprex_0.3.0 digest_0.6.25 webshot_0.5.2
## [85] munsell_0.5.0 viridisLite_0.3.0